Photon-added squeezed vacuum (one-photon) state as an even (odd) nonlinearcoherent state

We show that the photon-added squeezed vacuum a(dagger m)S(z)\0] and the ph oton-added squeezed one-photon state a dagger(m)S(z)\1], where in is a non- negative integer, may be regarded as even and odd nonlinear coherent states , respectively. To achieve this, we derive an operator-valued function f(N, m) of the number operator N = a(dagger)a such that a(dagger m)S(z)\i] (i = 0, 1) are eigenstates of f(N, m)a(2). Based on this, and using the unified method developed by Shanta et at, we find that a(dagger m)S(z)\i] can be e quivalently expressed in exponential forms. The eigenstates of f(N, -m)a(2) are also constructed and their nonclassical features are studied in detail .